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Question

Y(x,t)=0.05[(4x+2t)2+5] represents a moving wave pulse, where x and y are in meters and t is in seconds. Then which statement(s) are correct :

A
pluse is moving in x direction
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B
wave speed is 0.5m/s
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C
max. particle displacement is 1cm
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D
it is a symmetric pulse
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Solution

The correct options are
A pluse is moving in x direction
B wave speed is 0.5m/s
C max. particle displacement is 1cm
D it is a symmetric pulse
Given:
Y(x,t)=0.05(4x+2t)2+5
The general equation for a wave is given by f(ωtkx)=Y(x,t);
Comparing with the given equation we get ω=2rads1
and k=4m1
v=ωk
v=0.5ms1 (negative sign indicates travel in negative x direction)
The function obtains maximum displacement when (4x+2t) vanishes (=0)
At this point the displacement is 0.055=0.01m=1cm
We can also see that
Y(δt2,t)=Y(δt2,t)
What this implies is that the function Y(x,t) is symmetric about x=t2
Hence the pulse is symmetric.

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